# Project Euler 663: Sums of Subarrays
# Segment tree with block decomposition for maximum subarray sum.
# S(n, 10^7) to S(n, 10^7+200000) difference, n=10000003.
import euler.nt { isqrt }
extern {
function calloc(n: i64, size: i64) -> ptr<void>
function free(p: ptr<void>) -> void
}
const NEG_INF: i64 = -1000000000000000000
function max3(a: i64, b: i64, c: i64) -> i64 {
let mut m: i64 = a
if b > m { m = b }
if c > m { m = c }
return m
}
function max2(a: i64, b: i64) -> i64 {
if a >= b { return a }
return b
}
function main() -> i32 {
let n: i64 = 10000003
let start_step: i64 = 10000000
let end_step: i64 = 10200000
let B: i64 = 256
# Allocate array A
let A: ptr<i64> = calloc(n, 8)
if A == null { return 1 }
# Segment tree arrays
let m: i64 = (n + B - 1) / B
let mut size: i64 = 1
while size < m { size = size * 2 }
let tree_total: ptr<i64> = calloc(2 * size, 8)
let tree_pref: ptr<i64> = calloc(2 * size, 8)
let tree_suff: ptr<i64> = calloc(2 * size, 8)
let tree_best: ptr<i64> = calloc(2 * size, 8)
# Initialize tree_pref and tree_best to NEG_INF
for i in 0..(2 * size) {
tree_pref[i] = NEG_INF
tree_suff[i] = NEG_INF
tree_best[i] = NEG_INF
}
# Tribonacci mod n window: u0, u1, u2 for k=2i-2, 2i-1, 2i
let mut u0: i64 = 0
let mut u1: i64 = 0
let mut u2: i64 = 1 % n
let mut ans: i64 = 0
let mut tree_built: i64 = 0
for i in 1..(end_step + 1) {
let idx: i64 = u0
let delta: i64 = (u1 << 1) - n + 1
A[idx] = A[idx] + delta
if i == start_step {
# Build segment tree
# Compute block summaries for leaves
for b in 0..m {
let s: i64 = b * B
let e: i64 = n
if s + B < e { e = s + B }
if s >= n { e = s }
# block_summary(A, s, e)
let mut r: i64 = 0
let mut max_pref: i64 = NEG_INF
let mut min_pref_best: i64 = 0
let mut best: i64 = NEG_INF
let mut min_pref_suff: i64 = 0
let last: i64 = e - 1
for k in s..e {
r = r + A[k]
if r > max_pref { max_pref = r }
let cand: i64 = r - min_pref_best
if cand > best { best = cand }
if r < min_pref_best { min_pref_best = r }
if k != last {
if r < min_pref_suff { min_pref_suff = r }
}
}
let total_val: i64 = r
let max_suff: i64 = total_val - min_pref_suff
let pos: i64 = size + b
tree_total[pos] = total_val
tree_pref[pos] = max_pref
tree_suff[pos] = max_suff
tree_best[pos] = best
}
# Build internal nodes
for pos in 1..size {
let rev_pos: i64 = size - pos
let l: i64 = rev_pos * 2
let r_child: i64 = l + 1
tree_total[rev_pos] = tree_total[l] + tree_total[r_child]
let v1p: i64 = tree_pref[l]
let v2p: i64 = tree_total[l] + tree_pref[r_child]
tree_pref[rev_pos] = max2(v1p, v2p)
let v1s: i64 = tree_suff[r_child]
let v2s: i64 = tree_total[r_child] + tree_suff[l]
tree_suff[rev_pos] = max2(v1s, v2s)
tree_best[rev_pos] = max3(tree_best[l], tree_best[r_child], tree_suff[l] + tree_pref[r_child])
}
tree_built = 1
} else {
if i > start_step && tree_built == 1 {
# Update block containing idx
let b: i64 = idx / B
let s: i64 = b * B
let e: i64 = n
if s + B < e { e = s + B }
if s >= n { e = s }
# Recompute block summary
let mut r: i64 = 0
let mut max_pref: i64 = NEG_INF
let mut min_pref_best: i64 = 0
let mut best: i64 = NEG_INF
let mut min_pref_suff: i64 = 0
let last: i64 = e - 1
for k in s..e {
r = r + A[k]
if r > max_pref { max_pref = r }
let cand: i64 = r - min_pref_best
if cand > best { best = cand }
if r < min_pref_best { min_pref_best = r }
if k != last {
if r < min_pref_suff { min_pref_suff = r }
}
}
let total_val: i64 = r
let max_suff: i64 = total_val - min_pref_suff
let pos: i64 = size + b
tree_total[pos] = total_val
tree_pref[pos] = max_pref
tree_suff[pos] = max_suff
tree_best[pos] = best
# Update path to root
let mut p: i64 = pos / 2
while p >= 1 {
let l: i64 = p * 2
let r_child: i64 = l + 1
tree_total[p] = tree_total[l] + tree_total[r_child]
let v1p: i64 = tree_pref[l]
let v2p: i64 = tree_total[l] + tree_pref[r_child]
tree_pref[p] = max2(v1p, v2p)
let v1s: i64 = tree_suff[r_child]
let v2s: i64 = tree_total[r_child] + tree_suff[l]
tree_suff[p] = max2(v1s, v2s)
tree_best[p] = max3(tree_best[l], tree_best[r_child], tree_suff[l] + tree_pref[r_child])
p = p / 2
}
# Root best is at index 1
ans = ans + tree_best[1]
}
}
# Advance tribonacci by two steps (mod n)
let mut t3: i64 = u0 + u1 + u2
if t3 >= n { t3 = t3 - n }
if t3 >= n { t3 = t3 - n }
let mut t4: i64 = u1 + u2 + t3
if t4 >= n { t4 = t4 - n }
if t4 >= n { t4 = t4 - n }
u0 = u2
u1 = t3
u2 = t4
}
printf("%lld\n", ans)
free(tree_best)
free(tree_suff)
free(tree_pref)
free(tree_total)
free(A)
return 0
}
Generated C
#include <stdint.h>
#include <stdbool.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
/* Flow runtime helpers */
typedef struct flow_temp_node { struct flow_temp_node* next; } flow_temp_node;
static flow_temp_node* flow_temp_head = NULL;
static int flow_temp_atexit_set = 0;
__attribute__((unused)) static void flow_temp_free_all(void) {
while (flow_temp_head) {
flow_temp_node* n = flow_temp_head;
flow_temp_head = n->next;
free(n);
}
}
__attribute__((unused)) static void* flow_temp_alloc(size_t nbytes) {
flow_temp_node* node = (flow_temp_node*)malloc(sizeof(flow_temp_node) + nbytes);
if (!node) return NULL;
node->next = flow_temp_head;
flow_temp_head = node;
if (!flow_temp_atexit_set) {
flow_temp_atexit_set = 1;
atexit(flow_temp_free_all);
}
return (void*)(node + 1);
}
#ifndef FLOW_DIAG
#define FLOW_DIAG(msg) fprintf(stderr, "%s", (msg))
#endif
#ifndef FLOW_LOG
#define FLOW_LOG(fmt, ...) printf(fmt, __VA_ARGS__)
#endif
#ifndef FLOW_LOG_EMPTY
#define FLOW_LOG_EMPTY(fmt) printf(fmt)
#endif
static char* flow_strcat(const char* a, const char* b) {
size_t la = strlen(a ? a : ""), lb = strlen(b ? b : "");
char* r = (char*)flow_temp_alloc(la + lb + 1);
if (!r) return NULL;
if (la) memcpy(r, a, la);
if (lb) memcpy(r + la, b, lb);
r[la + lb] = '\0';
return r;
}
#define __flow_in_arr(arr, val) __extension__ ({ \
int _found = 0; \
size_t _n = sizeof(arr)/sizeof((arr)[0]); \
for (size_t _i = 0; _i < _n; _i++) { \
if ((arr)[_i] == (val)) { _found = 1; break; } \
} _found; })
/* Unified fault handler (MISRA #279) — override with -DFLOW_FAULT_HANDLER=fn */
#ifndef FLOW_FAULT_HANDLER
__attribute__((unused)) static inline void flow_fault_handler(const char* msg) {
fprintf(stderr, "flow: %s\n", msg ? msg : "fault");
abort();
#if defined(__GNUC__) || defined(__clang__)
__builtin_unreachable();
#endif
}
#else
#define flow_fault_handler FLOW_FAULT_HANDLER
#endif
#define flow_div_by_zero_handler() flow_fault_handler("division by zero")
#define flow_shift_ub_handler() flow_fault_handler("invalid shift (amount out of range or left-shift of negative)")
#ifndef FLOW_CHECKED_DIV
#define FLOW_CHECKED_DIV(L, R) (((R) != 0) ? ((L) / (R)) : (flow_div_by_zero_handler(), (L) * 0))
#endif
#ifndef FLOW_CHECKED_MOD
#define FLOW_CHECKED_MOD(L, R) (((R) != 0) ? ((L) % (R)) : (flow_div_by_zero_handler(), (L) * 0))
#endif
#ifndef FLOW_CHECKED_SHL
#define FLOW_CHECKED_SHL(L, R) ((((R) >= 0) && ((unsigned long long)(R) < (sizeof(L) * 8ull)) && ((L) >= 0)) ? ((L) << (R)) : (flow_shift_ub_handler(), (L) * 0))
#endif
#ifndef FLOW_CHECKED_SHR
#define FLOW_CHECKED_SHR(L, R) ((((R) >= 0) && ((unsigned long long)(R) < (sizeof(L) * 8ull))) ? ((L) >> (R)) : (flow_shift_ub_handler(), (L) * 0))
#endif
#include <math.h>
void* _ui_state = NULL;
static inline float i32_to_f32(int32_t v) { return (float)v; }
/* Host stub for @gpu kernels (device codegen replaces this). */
static inline int32_t gpu_thread_id(void) { return 0; }
int64_t gcd_i64_i64(int64_t a0, int64_t b0);
int64_t lcm_i64_i64(int64_t a, int64_t b);
int64_t isqrt_i64(int64_t n);
int64_t mulmod_i64_i64_i64(int64_t a0, int64_t b0, int64_t mod);
int64_t mod_pow_i64_i64_i64(int64_t base, int64_t exp, int64_t mod);
bool is_prime_i64(int64_t n);
int64_t max3_i64_i64_i64(int64_t a, int64_t b, int64_t c);
int64_t max2_i64_i64(int64_t a, int64_t b);
int32_t main(void);
static const int64_t NEG_INF = (-1000000000000000000);
int64_t gcd_i64_i64(int64_t a0, int64_t b0) {
int64_t a = a0;
int64_t b = b0;
while (b != 0) {
int64_t t = FLOW_CHECKED_MOD((a), (b));
a = b;
b = t;
}
return a;
}
int64_t lcm_i64_i64(int64_t a, int64_t b) {
if ((a == 0 || b == 0)) {
return 0;
}
return (FLOW_CHECKED_DIV((a), (gcd_i64_i64(a, b))) * b);
}
int64_t isqrt_i64(int64_t n) {
if (n < 2) {
return n;
}
int64_t x = n;
int64_t y = FLOW_CHECKED_DIV(((x + 1)), (2));
while (y < x) {
x = y;
y = FLOW_CHECKED_DIV(((x + FLOW_CHECKED_DIV((n), (x)))), (2));
}
return x;
}
int64_t mulmod_i64_i64_i64(int64_t a0, int64_t b0, int64_t mod) {
int64_t a = FLOW_CHECKED_MOD((a0), (mod));
int64_t b = FLOW_CHECKED_MOD((b0), (mod));
int64_t result = 0;
while (b > 0) {
if (FLOW_CHECKED_MOD((b), (2)) == 1) {
result = FLOW_CHECKED_MOD(((result + a)), (mod));
}
a = FLOW_CHECKED_MOD(((a * 2)), (mod));
b = FLOW_CHECKED_DIV((b), (2));
}
return result;
}
int64_t mod_pow_i64_i64_i64(int64_t base, int64_t exp, int64_t mod) {
if (mod == 1) {
return 0;
}
int64_t result = 1;
int64_t b = FLOW_CHECKED_MOD((base), (mod));
int64_t e = exp;
while (e > 0) {
if (FLOW_CHECKED_MOD((e), (2)) == 1) {
result = mulmod_i64_i64_i64(result, b, mod);
}
b = mulmod_i64_i64_i64(b, b, mod);
e = FLOW_CHECKED_DIV((e), (2));
}
return result;
}
bool is_prime_i64(int64_t n) {
if (n < 2) {
return 0;
}
if (n < 4) {
return 1;
}
if ((FLOW_CHECKED_MOD((n), (2)) == 0 || FLOW_CHECKED_MOD((n), (3)) == 0)) {
return 0;
}
int64_t i = 5;
while ((i * i) <= n) {
if ((FLOW_CHECKED_MOD((n), (i)) == 0 || FLOW_CHECKED_MOD((n), ((i + 2))) == 0)) {
return 0;
}
i = (i + 6);
}
return 1;
}
int64_t max3_i64_i64_i64(int64_t a, int64_t b, int64_t c) {
int64_t m = a;
if (b > m) {
m = b;
}
if (c > m) {
m = c;
}
return m;
}
int64_t max2_i64_i64(int64_t a, int64_t b) {
if (a >= b) {
return a;
}
return b;
}
int32_t main(void) {
int64_t n = 10000003;
int64_t start_step = 10000000;
int64_t end_step = 10200000;
int64_t B = 256;
int64_t* A = (int64_t*)(calloc(n, 8));
if (A == NULL) {
return 1;
}
int64_t m = FLOW_CHECKED_DIV((((n + B) - 1)), (B));
int64_t size = 1;
while (size < m) {
size = (size * 2);
}
int64_t* tree_total = (int64_t*)(calloc((2 * size), 8));
int64_t* tree_pref = (int64_t*)(calloc((2 * size), 8));
int64_t* tree_suff = (int64_t*)(calloc((2 * size), 8));
int64_t* tree_best = (int64_t*)(calloc((2 * size), 8));
int32_t __flow_step_1 = 1;
for (int32_t i = 0; (0 <= (2 * size)) ? i < (2 * size) : i > (2 * size); i += (0 <= (2 * size)) ? 1 : -1) {
tree_pref[i] = NEG_INF;
tree_suff[i] = NEG_INF;
tree_best[i] = NEG_INF;
}
int64_t u0 = 0;
int64_t u1 = 0;
int64_t u2 = FLOW_CHECKED_MOD((1), (n));
int64_t ans = 0;
int64_t tree_built = 0;
int32_t __flow_step_2 = 1;
for (int32_t i = 1; (1 <= (end_step + 1)) ? i < (end_step + 1) : i > (end_step + 1); i += (1 <= (end_step + 1)) ? 1 : -1) {
int64_t idx = u0;
int64_t delta = ((FLOW_CHECKED_SHL((u1), (1)) - n) + 1);
A[idx] = (A[idx] + delta);
if (i == start_step) {
int32_t __flow_step_3 = 1;
for (int32_t b = 0; (0 <= m) ? b < m : b > m; b += (0 <= m) ? 1 : -1) {
int64_t s = (b * B);
int64_t e = n;
if ((s + B) < e) {
e = (s + B);
}
if (s >= n) {
e = s;
}
int64_t r = 0;
int64_t max_pref = NEG_INF;
int64_t min_pref_best = 0;
int64_t best = NEG_INF;
int64_t min_pref_suff = 0;
int64_t last = (e - 1);
int32_t __flow_step_4 = 1;
for (int32_t k = s; (s <= e) ? k < e : k > e; k += (s <= e) ? 1 : -1) {
r = (r + A[k]);
if (r > max_pref) {
max_pref = r;
}
int64_t cand = (r - min_pref_best);
if (cand > best) {
best = cand;
}
if (r < min_pref_best) {
min_pref_best = r;
}
if (k != last) {
if (r < min_pref_suff) {
min_pref_suff = r;
}
}
}
int64_t total_val = r;
int64_t max_suff = (total_val - min_pref_suff);
int64_t pos = (size + b);
tree_total[pos] = total_val;
tree_pref[pos] = max_pref;
tree_suff[pos] = max_suff;
tree_best[pos] = best;
}
int32_t __flow_step_5 = 1;
for (int32_t pos = 1; (1 <= size) ? pos < size : pos > size; pos += (1 <= size) ? 1 : -1) {
int64_t rev_pos = (size - pos);
int64_t l = (rev_pos * 2);
int64_t r_child = (l + 1);
tree_total[rev_pos] = (tree_total[l] + tree_total[r_child]);
int64_t v1p = tree_pref[l];
int64_t v2p = (tree_total[l] + tree_pref[r_child]);
tree_pref[rev_pos] = max2_i64_i64(v1p, v2p);
int64_t v1s = tree_suff[r_child];
int64_t v2s = (tree_total[r_child] + tree_suff[l]);
tree_suff[rev_pos] = max2_i64_i64(v1s, v2s);
tree_best[rev_pos] = max3_i64_i64_i64(tree_best[l], tree_best[r_child], (tree_suff[l] + tree_pref[r_child]));
}
tree_built = 1;
} else {
if ((i > start_step && tree_built == 1)) {
int64_t b = FLOW_CHECKED_DIV((idx), (B));
int64_t s = (b * B);
int64_t e = n;
if ((s + B) < e) {
e = (s + B);
}
if (s >= n) {
e = s;
}
int64_t r = 0;
int64_t max_pref = NEG_INF;
int64_t min_pref_best = 0;
int64_t best = NEG_INF;
int64_t min_pref_suff = 0;
int64_t last = (e - 1);
int32_t __flow_step_6 = 1;
for (int32_t k = s; (s <= e) ? k < e : k > e; k += (s <= e) ? 1 : -1) {
r = (r + A[k]);
if (r > max_pref) {
max_pref = r;
}
int64_t cand = (r - min_pref_best);
if (cand > best) {
best = cand;
}
if (r < min_pref_best) {
min_pref_best = r;
}
if (k != last) {
if (r < min_pref_suff) {
min_pref_suff = r;
}
}
}
int64_t total_val = r;
int64_t max_suff = (total_val - min_pref_suff);
int64_t pos = (size + b);
tree_total[pos] = total_val;
tree_pref[pos] = max_pref;
tree_suff[pos] = max_suff;
tree_best[pos] = best;
int64_t p = FLOW_CHECKED_DIV((pos), (2));
while (p >= 1) {
int64_t l = (p * 2);
int64_t r_child = (l + 1);
tree_total[p] = (tree_total[l] + tree_total[r_child]);
int64_t v1p = tree_pref[l];
int64_t v2p = (tree_total[l] + tree_pref[r_child]);
tree_pref[p] = max2_i64_i64(v1p, v2p);
int64_t v1s = tree_suff[r_child];
int64_t v2s = (tree_total[r_child] + tree_suff[l]);
tree_suff[p] = max2_i64_i64(v1s, v2s);
tree_best[p] = max3_i64_i64_i64(tree_best[l], tree_best[r_child], (tree_suff[l] + tree_pref[r_child]));
p = FLOW_CHECKED_DIV((p), (2));
}
ans = (ans + tree_best[1]);
}
}
int64_t t3 = ((u0 + u1) + u2);
if (t3 >= n) {
t3 = (t3 - n);
}
if (t3 >= n) {
t3 = (t3 - n);
}
int64_t t4 = ((u1 + u2) + t3);
if (t4 >= n) {
t4 = (t4 - n);
}
if (t4 >= n) {
t4 = (t4 - n);
}
u0 = u2;
u1 = t3;
u2 = t4;
}
printf("%lld\n", ans);
free(tree_best);
free(tree_suff);
free(tree_pref);
free(tree_total);
free(A);
return 0;
}